document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971000>Question 971000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Show that 2 + (the square root) of 2i and 2-(the square root) of 2i satisfy the equation x^2 - 4x + 6 = 0. \r<BR>\n" );
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document.write( "2. Solve and check: (please be clear)<BR>\n" );
document.write( "a) x^2 +4 = 0<BR>\n" );
document.write( "b) x^2 +12 = 0<BR>\n" );
document.write( "c) x^2 -2x + 2 = 0\r<BR>\n" );
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document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593627 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 -4 x +6=0\r<BR>\n" );
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document.write( "The roots are  2 +/- i (sqrt 2), which is different from the sqrt (2i) which doesn't work and isn't found by the quadratic formula (see below).\r<BR>\n" );
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document.write( "(2 + i sqrt (2)) ^2  -4 (2 +i sqrt (2))   +6=\r<BR>\n" );
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document.write( "4 + 4i^1/2  + 2i^2  -8 -4i ^1/2 +6=   The 4i (sqrt (2)) disappear, and i^2=-1\r<BR>\n" );
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document.write( "4+ (-2) -8+6=0\r<BR>\n" );
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document.write( "2- i (sqrt 2) does the same thing only the signs change in the first term and in the second term.\r<BR>\n" );
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document.write( "quadratic formula\r<BR>\n" );
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document.write( "a=1  b=-4  c=6\r<BR>\n" );
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document.write( "x= [4 +/- sqrt (16-24)]/2]\r<BR>\n" );
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document.write( "x={4 +/- sqrt (-8)}/2} = {4 +/- sqrt (-4)*(2)]/2} = 2 +/- (2 i *sqrt (2), after dividing all by 2.\r<BR>\n" );
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document.write( "x= 2 +/- i sqrt(2)<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "x^2=-4 ;  x= +/- 2i  ; (2i)^2 is 4 i^2=-4 ; i^2=-1  ; For minus 2i, the square removes the negative.\r<BR>\n" );
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document.write( "x^2=-12;   x= +/- sqrt (-4)* sqrt (3)= +/- 2i sqrt (3).  This squares to 4i^2 *3=-12<BR>\n" );
document.write( "x^2-2x-2\r<BR>\n" );
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document.write( "(1/2) {2 +/- sqrt (4-8)}  = (1/2) 2 +/- sqrt (-4) = (1/2) 2 +/- 2i = 1+/- i\r<BR>\n" );
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document.write( "(1+  i )^2 -2(1+i) +2<BR>\n" );
document.write( "=1 +2 i + i^2 -2 -2i +2<BR>\n" );
document.write( "=1 +2i -1 -2 -21 +2<BR>\n" );
document.write( "=0 </SPAN>\n" );
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